Adaptive EWMA procedures for monitoring processes subject to linear drifts

• Published in: Computational statistics & data analysis Vol. 55; no. 10; pp. 2819 - 2829
• Main Authors: Su, Yan, Shu, Lianjie, Tsui, Kwok-Leung
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.10.2011; Elsevier
• Series: Computational Statistics & Data Analysis
• Subjects: Average run length; Average run length Integral equation Linear trend Statistical Process Control Exponentially weighted moving average; Charts; Computation; Drift; Exact sciences and technology; Exponentially weighted moving average; General topics; Guidelines; Integral equation; Linear trend; Mathematics; Monitoring; Multivariate analysis; Numerical analysis; Numerical analysis. Scientific computation; Numerical approximation; Numerical methods in probability and statistics; Probability and statistics; Sciences and techniques of general use; Statistical Process Control; Statistics; Tool wear; Integral equation; Exponentially weighted moving average; Statistical Process Control; Average run length; Linear trend; Statistical process control; Data analysis; Numerical integration; Moving average; Statistical estimation; Computing; Mean estimation; Numerical approximation; Linear process; Statistical computation; Experimental design
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2011.04.008

The conventional Statistical Process Control (SPC) techniques have been focused mostly on the detection of step changes in process means. However, there are often settings for monitoring linear drifts in process means, e.g., the gradual change due to tool wear or similar causes. The adaptive exponentially weighted moving average (AEWMA) procedures proposed by  Yashchin (1995) have received a great deal of attention mainly for estimating and monitoring step mean shifts. This paper analyzes the performance of AEWMA schemes in signaling linear drifts. A numerical procedure based on the integral equation approach is presented for computing the average run length (ARL) of AEWMA charts under linear drifts in the mean. The comparison results favor the AEWMA chart under linear drifts. Some guidelines for designing AEWMA charts for detecting linear drifts are presented.